feat(QuantumMechanics/Blackbody): extend Planck's law with wavelength form and radiation constants by dwan-ith · Pull Request #1720 · leanprover-community/physlib

dwan-ith · 2026-10-02T13:02:26Z

Formalizes the project idea "Planck's Theory of Blackbody Radiation" from physlib.io/project-ideas.

Extends the existing Physlib.QuantumMechanics.Blackbody.PlancksLaw

Planck's Law:

Parametrized spectral radiance per unit frequency (spectralRadianceFreq) and wavelength (spectralRadianceWave)
Correspondence theorem spectralRadianceWave_eq_freq: $B(\lambda, T) = (c/\lambda^2) B(\nu = c/\lambda, T)$
First and second radiation constants ($c_{1L} = 2hc^2$, $c_2 = hc/k_B$) with spectralRadianceWave_eq_constants
Positivity, absolute-zero vanishing, and boundary lemmas

(Note: Wien's displacement law has been done as a seperate PR).

…isplacement law Formalizes the project idea 'Planck's Theory of Blackbody Radiation' from https://physlib.io/project-ideas. Key additions: - Frequency and wavelength forms of Planck's spectral radiance - Positivity, absolute-zero limits, correspondence between forms - First and second radiation constants - Wien auxiliary function h(x) = x - n(1 - e^{-x}) - Existence and uniqueness of the positive Wien root (IVT + monotonicity) - Named Wien constants x5 ≈ 4.9651 (wavelength) and x3 ≈ 2.8214 (frequency) - Rigorous enclosures 4 < x5 < 5 and 2 < x3 < 3 (no sorry) - Global maxima of spectral radiance curves (isMaxOn) - Wien's displacement laws: λ₁T₁ = λ₂T₂ and ν₁/T₁ = ν₂/T₂ - Proof that wavelength and frequency peaks differ (wien_roots_differ)

github-actions · 2026-10-02T13:03:06Z

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jstoobysmith · 2026-10-02T13:08:29Z

Hi @dwan-ith Many thanks for this Pull-request (PR). I think this is a bit long. Maybe we could restrict this PR to just be the Planck's law file? This way we can iterate a lot quicker :).

jstoobysmith · 2026-10-02T13:08:36Z

awaiting-author

dwan-ith · 2026-10-02T13:27:42Z

Hi Joseph. Sure thing, I will do only Planck's law. The rest in another PR or how would you like it to be done?

jstoobysmith · 2026-10-02T13:28:52Z

Yes please, if the rest could go in another PR that would be great.

jstoobysmith

Couple of comments to start of with

jstoobysmith · 2026-10-02T13:37:33Z

@@ -1,13 +1,14 @@
 /-
-Copyright (c) 2026 Samyak Rai. All rights reserved.
+Copyright (c) 2026 Samyak Rai, Dwanith C. Jayanth. All rights reserved.


Normally we restrict the copyright to only one name.

jstoobysmith · 2026-10-02T13:46:55Z

+    `B(ν, T) = 2 h ν³ / c² · 1 / (e ^ (h ν / (kB T)) - 1)`,
+
+  extended by zero outside the physical domain. -/
+noncomputable def spectralRadianceFreq (h c kB ν T : ℝ) : ℝ :=


I wouldn't remake this definition since it is essentially equivalent to spectralRadiance.

jstoobysmith · 2026-10-02T13:47:37Z


 @[expose] public section

-


Here I think it might be worth making a structure

structure BlackBody with T : Temperature

and then using this as an input to all of the things bellow.

jstoobysmith · 2026-10-02T13:50:19Z

+-/
+
+/-- The first radiation constant `c₁L = 2 h c²`. -/
+noncomputable def firstRadiationConstant (h c : ℝ) : ℝ := 2 * h * c ^ 2


c : SpeedOfLight. We also use the value of kB and h given via the imports. In theory we could define a set value of c aswell.

jstoobysmith · 2026-10-02T13:50:48Z

+  le_of_lt (spectralRadianceFreq_pos h c kB ν T hh hc hk hν hT)
+
+/-- The spectral radiance per unit wavelength is non-negative on the physical domain. -/
+lemma spectralRadianceWave_nonneg (h c kB lam T : ℝ) (hh : 0 < h) (hc : 0 < c)


Results like this should appear next to the corresponding definition.

jstoobysmith · 2026-10-02T13:51:10Z

+
+/-- The first radiation constant equals `2 * h * c ^ 2`. -/
+@[simp]
+lemma firstRadiationConstant_eq (h c : ℝ) :


I probably would not attribute this and the lemma below with @[simp].

jstoobysmith · 2026-10-02T13:51:31Z

awaiting-author

dwan-ith · 2026-10-02T13:53:40Z

sorry, this is my first PR. but sure, i'll make all the changes

jstoobysmith · 2026-10-02T14:02:09Z

@dwan-ith responding to your email - no need to apologise! Totally normal for lots of comments on PRs (even experienced contributors get them :)).

jstoobysmith · 2026-10-02T14:04:23Z

There are some design decisions which likely need to be addressed at some point, if this is of interest to you (not necessary for this PR). For example, do we need a type for frequency, and wavelength (we currently don't). Do we need a type for things like the planck's constant as we do with SpeedOfLight (currently we just have a given element). These two approaches don't appear to agree....

dwan-ith · 2026-10-02T14:14:18Z

Thanks for pointing that out! I noticed them too. some were a bit confusing and probably need to be sorted out as you said. let me know if there's anything else that needs adjusting! :)

github-actions Bot added the large label Oct 2, 2026

github-actions Bot added the t-quantum-mechanics Quantum mechanics label Oct 2, 2026

github-actions Bot added the awaiting-author A reviewer has asked the author a question or requested changes label Oct 2, 2026

refactor: restrict PR to Planck's law file

1d10828

github-actions Bot added medium and removed large labels Oct 2, 2026

dwan-ith changed the title ~~feat(QuantumMechanics/Blackbody): formalize Planck's law and Wien's displacement law~~ feat(QuantumMechanics/Blackbody): extend Planck's law with wavelength form and radiation constants Oct 2, 2026

github-actions Bot removed the awaiting-author A reviewer has asked the author a question or requested changes label Oct 2, 2026

jstoobysmith reviewed Oct 2, 2026

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github-actions Bot added the awaiting-author A reviewer has asked the author a question or requested changes label Oct 2, 2026

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